The Pauli principle, normal modes and superfluidity: the emergence of collective organizational phenomena

TL;DR

This paper introduces a symmetry invariant perturbation theory approach to explain superfluidity emergence in fermionic systems, highlighting the role of the Pauli principle and normal modes in collective behavior.

Contribution

It presents a novel first-order perturbation method using group theory to identify collective normal modes and explain superfluidity driven by quantum statistics.

Findings

Normal modes include breathing, center of mass, and phonons.

Occupation occurs mainly in a low-frequency phonon mode at ultralow temperatures.

The model's predictions align with experimental thermodynamic data, including the lambda transition.

Abstract

Understanding the emergence of collective organizational phenomena is a major goal in many fields of physics from condensed matter to cosmology. Using a recently introduced manybody perturbation formalism for fermions, we propose a mechanism for the emergence of collective behavior, specifically superfluidity, driven by quantum statistics and the enforcement of the Pauli principle through the selection of normal modes. The method, which is called symmetry invariant perturbation theory (SPT), uses group theory and graphical techniques to solve the manybody Schrodinger equation through first order exactly. The solution at first order defines collective coordinates in terms of five N-body normal modes, identified as breathing, center of mass, single particle angular excitation, single particle radial excitation and phonon. A correspondence is established "on paper" that enforces the Pauli principle through the assignment of specific normal mode quantum numbers. Applied in the unitary regime, this normal mode assignment yields occupation only in an extremely low frequency N-body phonon mode at ultralow temperatures. A single particle radial excitation mode at a much higher frequency creates a gap that stabilizes the superfluidity at low temperatures. Coupled with the corresponding values for the frequencies at unitarity obtained by this manybody calculation, we obtain good agreement with experimental thermodynamic results including the lambda transition in the specific heat. Our results suggest that the emergence of collective behavior in macroscopic systems is driven by the Pauli principle and its selection of the correct collective coordinates in the form of N-body normal modes.